# Identification and analysis of the connection network structure between the components of the immune system in children

## TL;DR

This study explores the network connections between immune system components in young children using a statistical method to handle small sample sizes.

## Contribution

The paper introduces the use of the DSPC algorithm to analyze immune system networks in children with limited data.

## Key findings

- The choice of statistical significance threshold strongly affects the network structure with small sample sizes.
- Graph visualization and topological analysis revealed key relationships between immune cells, cytokines, and antibodies.
- Larger sample sizes and mechanistic models are needed to confirm the network's immunological accuracy.

## Abstract

Identification of the connections between the various functional components of the immune system is a crucial task in modern immunology. It is key to implementing the systems biology approach to understand the mechanisms of dynamic changes and outcomes of infectious and oncological diseases. The data characterizing an individual’s immune status typically have a high-dimensional state space and a small sample size. To study the network topology of the immune system, we utilized previously published original data from Toptygina et al. (2023), which included measurements of the immune status in 19 healthy individuals (children, 9 boys and 10 girls, aged 1 to 2 years), i. e., the immune cells (42 subpopulations) obtained by flow cytometry; cytokine levels (13 types) obtained by multiplex analysis; and antibody levels (4 types) determined by using enzyme immunoassay. To correctly identify statistically significant correlations between the measured variables and construct the respective network graph, it is necessary to use an approach that takes into account the small size of the dataset. In this study, we implemented and analyzed an approach based on the regularized debiased sparse partial correlation (DSPC) algorithm to evaluate sparse partial correlations and identify the network structure of relationships in the immune system of healthy individuals (children) based on immune status data, which includes a set of indicators for subpopulations of immune cells, cytokine levels, and antibodies. For different levels of statistical significance, heatmaps of the partial correlations were constructed. The graph visualization of the DSPC networks was performed, and their topological characteristics were analyzed. It is found that with a limited measurements sample, the choice of a statistical significance threshold critically affects the structure of the partial correlations matrix. The final verification of the immunologically correct structure of the correlation-based network requires both an increase in the sample size and consideration of a priori mechanistic views and models of the functioning of the immune system components. The results of this analysis can be used to select the therapy targets and design combination therapies.